Application Of The Telegraph Equation To Oceanic Diffusion: Another Mathematic model

Abstract: The solution of the conventional diffusion equation has an obvious shortcoming; that is, the substance concentration will rise instantaneously everywhere when substance is introduced at some point in the sea. Although such instantaneous propagation of substance makes a negligibly small contribution to the concentration at large distances from the source, it might cause serious error in predicting water pollution, micro-organism distributions, etc. A diffusion equation which overcomes this difficulty is the telegraph equation characterized by a finite propagation velocity. An ad hoc derivation of the telegraph equation from a set of hydromechanical equations identifies the parameters involved in the equation. Thus, the propagation velocity is related to the correlation tensor of turbulent velocity. As a result, the one-particle dispersion law by Taylor and the relative diffusion law by Richardson can be deduced from the telegraph equation.